Distributive rings and endodistributive modules (Q1080499)

A module M having a distributive lattice of submodules is called distributive. It is called endodistributive if it is distributive over the ring \(D=End M\). The author establishes the equivalence of the following conditions: (a) R is a distributive right R-module; (b) all injective right R-modules are endodistributive; (c) all direct products and direct sums of quasiinjective right R-modules are endodistributive; (d) all injective envelopes of simple right R-modules are endodistributive. If the right maximal ring of quotients Q of a right distributive ring R is right selfinjective, then Q is left distributive. This result is applied for Noetherian rings and Dedekind domains.